Using Mean, Median and the Mode
Understanding Statistics using Foreclosure as an Example
An example of the differences in mean, median and mode, using an example from the housing industry.
When reviewing statistics, it is important to understand the definitions of the term used. The terms mean and median are often misunderstood and misused. The correct usage can be illustrated by an example on house sales.
Mean, Median and Mode
The mean of any distribution is the average of all the values added together. This is computed by taking all the values and adding them together, and dividing by the number of values.
A Median is the middle number of the distribution. The Mode is the term for the value that occurs most often in the distribution.
Consider the distribution with five values:
2, 2, 4, 8, 9
The mean, or average, of this distribution is 5, derived by adding the values to get 25 and dividing by number of values. The medium is 4, since the middle number (the third number) is 4.
The mode of this distribution is 2, since that value occurs twice and all the other values occur only once.
Means, or averages, need to be based on numbers.
Statistics in the Foreclosure Crisis
Mark Twain said that there are lies, damned lies and statistics. When looking at the housing crisis, it is important to understand how statistics can be misleading.
Housing prices are compared from year to year, often comparing the median selling price of a house from one year to the next, and using the change in prices to judge the performance of the housing market.
A drawback to this method is that median prices of homes sold only measure the value of those particular homes, not the entire market.
For example, if in year one, three homes were sold for the prices of $30,000, $50,000 and $100,000. In year two in the example, again, three homes could have sold. Two homes sold at foreclosure for $20,000 and one very nice house for $200,000.
The median price of the homes declined 60% ($50,000 to $20,000), but the mean price actually went up from $60,000 to $80,000.
The Importance of Statistics
In the above example, a person could make a case for houses going up or down in value, based on whether they used the mean or median.
Another opinion might be that considering all factors, the mode might be the best indicator in this case, since it shows that the greatest number sold for a significantly lower price than the average.
A reader that is aware of the different statistical measurements will be in a better position to make an informed judgment.
